LMFDB - Embedded newform 3.41.b.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,41,Mod(2,3)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 41, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 41);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 41 $
Character orbit:	$[\chi]$	$=$	3.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$30.4026855589$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 249659905422 x^{10} + \cdots + 12\!\cdots\!00 $ x^12 + 249659905422x^10 + 21357900831219724160448x^8 + 757005714875983264074654770397184x^6 + 10196659004511185116272142565764285511761920x^4 + 42071301184141474816096210166597335428414342325862400*x^2 + 12606130133749306378798090199763505554693706712963960799232000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{63}\cdot 3^{98}\cdot 5^{6}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.4
Root			$-127140. i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.41.b.a.2.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-762842. i q^{2} +(3.30429e9 + 1.11325e9i) q^{3} +5.17583e11 q^{4} +7.70076e13i q^{5} +(8.49232e14 - 2.52065e15i) q^{6} -3.01966e15 q^{7} -1.23359e18i q^{8} +(9.67903e18 + 7.35699e18i) q^{9} +O(q^{10})$	\(q-762842. i q^{2} +(3.30429e9 + 1.11325e9i) q^{3} +5.17583e11 q^{4} +7.70076e13i q^{5} +(8.49232e14 - 2.52065e15i) q^{6} -3.01966e15 q^{7} -1.23359e18i q^{8} +(9.67903e18 + 7.35699e18i) q^{9} +5.87447e19 q^{10} -8.18632e20i q^{11} +(1.71025e21 + 5.76198e20i) q^{12} +1.15208e22 q^{13} +2.30352e21i q^{14} +(-8.57285e22 + 2.54456e23i) q^{15} -3.71945e23 q^{16} +7.23126e24i q^{17} +(5.61222e24 - 7.38357e24i) q^{18} +2.86951e25 q^{19} +3.98578e25i q^{20} +(-9.97783e24 - 3.36163e24i) q^{21} -6.24487e26 q^{22} -7.48501e25i q^{23} +(1.37329e27 - 4.07614e27i) q^{24} +3.16477e27 q^{25} -8.78853e27i q^{26} +(2.37922e28 + 3.50848e28i) q^{27} -1.56292e27 q^{28} +1.79137e28i q^{29} +(1.94110e29 + 6.53973e28i) q^{30} +8.58238e29 q^{31} -1.07261e30i q^{32} +(9.11340e29 - 2.70500e30i) q^{33} +5.51631e30 q^{34} -2.32537e29i q^{35} +(5.00970e30 + 3.80785e30i) q^{36} +2.97963e31 q^{37} -2.18899e31i q^{38} +(3.80680e31 + 1.28255e31i) q^{39} +9.49957e31 q^{40} -3.27378e31i q^{41} +(-2.56439e30 + 7.61152e30i) q^{42} -7.95109e32 q^{43} -4.23710e32i q^{44} +(-5.66544e32 + 7.45359e32i) q^{45} -5.70989e31 q^{46} +2.08798e33i q^{47} +(-1.22902e33 - 4.14067e32i) q^{48} -6.35769e33 q^{49} -2.41422e33i q^{50} +(-8.05018e33 + 2.38942e34i) q^{51} +5.96295e33 q^{52} -5.75238e34i q^{53} +(2.67642e34 - 1.81497e34i) q^{54} +6.30409e34 q^{55} +3.72502e33i q^{56} +(9.48171e34 + 3.19448e34i) q^{57} +1.36653e34 q^{58} +7.76882e34i q^{59} +(-4.43716e34 + 1.31702e35i) q^{60} +3.24648e35 q^{61} -6.54700e35i q^{62} +(-2.92274e34 - 2.22156e34i) q^{63} -1.22719e36 q^{64} +8.87187e35i q^{65} +(-2.06349e36 - 6.95209e35i) q^{66} -2.79201e36 q^{67} +3.74278e36i q^{68} +(8.33267e34 - 2.47327e35i) q^{69} -1.77389e35 q^{70} +1.05889e37i q^{71} +(9.07549e36 - 1.19399e37i) q^{72} +6.07142e36 q^{73} -2.27299e37i q^{74} +(1.04573e37 + 3.52318e36i) q^{75} +1.48521e37 q^{76} +2.47199e36i q^{77} +(9.78381e36 - 2.90399e37i) q^{78} +3.31828e37 q^{79} -2.86426e37i q^{80} +(3.95583e37 + 1.42417e38i) q^{81} -2.49738e37 q^{82} -9.06890e37i q^{83} +(-5.16436e36 - 1.73992e36i) q^{84} -5.56862e38 q^{85} +6.06543e38i q^{86} +(-1.99424e37 + 5.91921e37i) q^{87} -1.00985e39 q^{88} -1.59950e39i q^{89} +(5.68591e38 + 4.32184e38i) q^{90} -3.47888e37 q^{91} -3.87412e37i q^{92} +(2.83587e39 + 9.55431e38i) q^{93} +1.59280e39 q^{94} +2.20974e39i q^{95} +(1.19408e39 - 3.54421e39i) q^{96} -3.49860e39 q^{97} +4.84991e39i q^{98} +(6.02267e39 - 7.92356e39i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots - 23\!\cdots\!20 q^{9}+O(q^{10}) $ 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9	$ 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots + 54\!\cdots\!80 q^{99}+O(q^{100}) $ 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9 - 129384136354706290080 * q^10 - 4708039830028985428272 * q^12 + 704368845864154901976 * q^13 + 320935800901459838631840 * q^15 + 6054431850962872672227456 * q^16 + 10227710367381761273509920 * q^18 + 37616619688417835612151720 * q^19 - 179163719456723608834234728 * q^21 + 846315150249292772829325920 * q^22 - 18213480358094369517645250944 * q^24 + 8842265325510151276196474700 * q^25 - 70717074113738779393083858252 * q^27 + 469404222007499612173589889696 * q^28 - 207809636542026559976510503200 * q^30 - 914600368399753689553849145016 * q^31 + 157344642221562801276041757600 * q^33 - 14575908480758621487300381842304 * q^34 + 41100171486790863962401658870544 * q^36 + 5673106137824212681873457220696 * q^37 - 9206461430638842876438079090008 * q^39 + 50495897877443363581635475618560 * q^40 - 939238658319640212873301303645920 * q^42 + 1012654832326802922602871229857576 * q^43 + 196109968512215856818385626472000 * q^45 - 3082500781506234684371181468390336 * q^46 + 6532128822166367998693520969705088 * q^48 + 8498166150175390075155260408801892 * q^49 + 27565453699222767413826960590504832 * q^51 - 57328509042562386918101767400001504 * q^52 - 102847607224782098537542351912875792 * q^54 - 9637639495259752880102706884884800 * q^55 - 40307213604482059940636368892395464 * q^57 + 772129436848561910287203884295052320 * q^58 - 114385571579949295944121547557720320 * q^60 - 494443282701607071691140418439862696 * q^61 + 1379291076525018665154441723571240776 * q^63 - 6231783699524672226208093043936541696 * q^64 + 2652084094607847915810184973553481440 * q^66 + 5401062423529881431761320436868275176 * q^67 + 7110274695178254111533494284632123328 * q^69 + 516103243900107216646679160954379200 * q^70 - 27544975046740790141119542770107057920 * q^72 + 30000154498324943042431295514883418136 * q^73 + 43820294796704764666539599709819928500 * q^75 - 215478934792040263381331019050660960352 * q^76 + 234946633516471169601955850003339878560 * q^78 - 128704557118405295534397879672035334840 * q^79 + 473157359902659920298963194247360443532 * q^81 - 639159997421964256448917103585883414720 * q^82 + 1283288903941350744781821238287455403552 * q^84 - 1077142486191382871466217243736209678080 * q^85 + 1076668306862385320797179121273520148960 * q^87 - 2918662713596496795370587920448329114880 * q^88 + 6571793457940570799819318674019816438880 * q^90 - 9859184204686878150356379414618151910256 * q^91 + 11506410044121210986218054652959643683416 * q^93 - 16857264118330945289191940748512432348544 * q^94 + 53068562519213731340201280418423192237056 * q^96 - 41841010071967618660163746722085070705064 * q^97 + 54341076855402233475300783474292013590080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	762842.i		−	0.727503i	−0.931496	−	0.363752i	$-0.881496\pi$
$2$		−	762842.i		−	0.727503i	0.931496	−	0.363752i	$-0.118504\pi$
$3$	3.30429e9	+	1.11325e9i	0.947662	+	0.319276i
$3$	3.30429e9	+	1.11325e9i	0.947662	+	0.319276i
$4$	5.17583e11			0.470739
$5$			7.70076e13i			0.807483i	0.914873	+	0.403742i	$0.132291\pi$
$5$			7.70076e13i			0.807483i	−0.914873	+	0.403742i	$0.867709\pi$
$6$	8.49232e14	−	2.52065e15i	0.232274	−	0.689427i
$7$	−3.01966e15			−0.0378440			−0.0189220	−	0.999821i	$-0.506023\pi$
$7$	−3.01966e15			−0.0378440			−0.0189220	+	0.999821i	$0.506023\pi$
$8$		−	1.23359e18i		−	1.06997i
$9$	9.67903e18	+	7.35699e18i	0.796125	+	0.605132i
$10$	5.87447e19			0.587447
$11$		−	8.18632e20i		−	1.21684i	−0.793614	−	0.608422i	$-0.791803\pi$
$11$		−	8.18632e20i		−	1.21684i	0.793614	−	0.608422i	$-0.208197\pi$
$12$	1.71025e21	+	5.76198e20i	0.446101	+	0.150296i
$13$	1.15208e22			0.606198			0.303099	−	0.952959i	$-0.401979\pi$
$13$	1.15208e22			0.606198			0.303099	+	0.952959i	$0.401979\pi$
$14$			2.30352e21i			0.0275316i
$15$	−8.57285e22	+	2.54456e23i	−0.257810	+	0.765221i
$16$	−3.71945e23			−0.307666
$17$			7.23126e24i			1.77924i	0.456698	+	0.889622i	$0.349032\pi$
$17$			7.23126e24i			1.77924i	−0.456698	+	0.889622i	$0.650968\pi$
$18$	5.61222e24	−	7.38357e24i	0.440235	−	0.579184i
$19$	2.86951e25			0.763372			0.381686	−	0.924292i	$-0.375344\pi$
$19$	2.86951e25			0.763372			0.381686	+	0.924292i	$0.375344\pi$
$20$			3.98578e25i			0.380114i
$21$	−9.97783e24	−	3.36163e24i	−0.0358633	−	0.0120827i
$22$	−6.24487e26			−0.885258
$23$		−	7.48501e25i		−	0.0436150i	−0.999762	−	0.0218075i	$-0.993058\pi$
$23$		−	7.48501e25i		−	0.0436150i	0.999762	−	0.0218075i	$-0.00694209\pi$
$24$	1.37329e27	−	4.07614e27i	0.341615	−	1.01397i
$25$	3.16477e27			0.347971
$26$		−	8.78853e27i		−	0.441011i
$27$	2.37922e28	+	3.50848e28i	0.561254	+	0.827644i
$28$	−1.56292e27			−0.0178146
$29$			1.79137e28i			0.101210i	0.998719	+	0.0506052i	$0.0161150\pi$
$29$			1.79137e28i			0.101210i	−0.998719	+	0.0506052i	$0.983885\pi$
$30$	1.94110e29	+	6.53973e28i	0.556701	+	0.187558i
$31$	8.58238e29			1.27754			0.638769	−	0.769399i	$-0.279444\pi$
$31$	8.58238e29			1.27754			0.638769	+	0.769399i	$0.279444\pi$
$32$		−	1.07261e30i		−	0.846140i
$33$	9.11340e29	−	2.70500e30i	0.388509	−	1.15316i
$34$	5.51631e30			1.29441
$35$		−	2.32537e29i		−	0.0305584i
$36$	5.00970e30	+	3.80785e30i	0.374767	+	0.284859i
$37$	2.97963e31			1.28863			0.644315	−	0.764760i	$-0.277143\pi$
$37$	2.97963e31			1.28863			0.644315	+	0.764760i	$0.277143\pi$
$38$		−	2.18899e31i		−	0.555356i
$39$	3.80680e31	+	1.28255e31i	0.574470	+	0.193545i
$40$	9.49957e31			0.863981
$41$		−	3.27378e31i		−	0.181707i	−0.995864	−	0.0908537i	$-0.971040\pi$
$41$		−	3.27378e31i		−	0.181707i	0.995864	−	0.0908537i	$-0.0289596\pi$
$42$	−2.56439e30	+	7.61152e30i	−0.00879019	+	0.0260907i
$43$	−7.95109e32			−1.70238			−0.851192	−	0.524854i	$-0.824120\pi$
$43$	−7.95109e32			−1.70238			−0.851192	+	0.524854i	$0.824120\pi$
$44$		−	4.23710e32i		−	0.572816i
$45$	−5.66544e32	+	7.45359e32i	−0.488634	+	0.642858i
$46$	−5.70989e31			−0.0317300
$47$			2.08798e33i			0.754692i	0.926072	+	0.377346i	$0.123163\pi$
$47$			2.08798e33i			0.754692i	−0.926072	+	0.377346i	$0.876837\pi$
$48$	−1.22902e33	−	4.14067e32i	−0.291563	−	0.0982303i
$49$	−6.35769e33			−0.998568
$50$		−	2.41422e33i		−	0.253150i
$51$	−8.05018e33	+	2.38942e34i	−0.568070	+	1.68612i
$52$	5.96295e33			0.285361
$53$		−	5.75238e34i		−	1.88075i	−0.340146	−	0.940373i	$-0.610476\pi$
$53$		−	5.75238e34i		−	1.88075i	0.340146	−	0.940373i	$-0.389524\pi$
$54$	2.67642e34	−	1.81497e34i	0.602114	−	0.408314i
$55$	6.30409e34			0.982582
$56$			3.72502e33i			0.0404918i
$57$	9.48171e34	+	3.19448e34i	0.723419	+	0.243727i
$58$	1.36653e34			0.0736309
$59$			7.76882e34i			0.297382i	0.988884	+	0.148691i	$0.0475060\pi$
$59$			7.76882e34i			0.297382i	−0.988884	+	0.148691i	$0.952494\pi$
$60$	−4.43716e34	+	1.31702e35i	−0.121361	+	0.360219i
$61$	3.24648e35			0.637993			0.318996	−	0.947756i	$-0.396654\pi$
$61$	3.24648e35			0.637993			0.318996	+	0.947756i	$0.396654\pi$
$62$		−	6.54700e35i		−	0.929413i
$63$	−2.92274e34	−	2.22156e34i	−0.0301286	−	0.0229006i
$64$	−1.22719e36			−0.923235
$65$			8.87187e35i			0.489495i
$66$	−2.06349e36	−	6.95209e35i	−0.838925	−	0.282642i
$67$	−2.79201e36			−0.840275			−0.420138	−	0.907460i	$-0.638018\pi$
$67$	−2.79201e36			−0.840275			−0.420138	+	0.907460i	$0.638018\pi$
$68$			3.74278e36i			0.837560i
$69$	8.33267e34	−	2.47327e35i	0.0139252	−	0.0413323i
$70$	−1.77389e35			−0.0222313
$71$			1.05889e37i			0.999270i	0.866236	+	0.499635i	$0.166533\pi$
$71$			1.05889e37i			0.999270i	−0.866236	+	0.499635i	$0.833467\pi$
$72$	9.07549e36	−	1.19399e37i	0.647471	−	0.851828i
$73$	6.07142e36			0.328725			0.164363	−	0.986400i	$-0.447443\pi$
$73$	6.07142e36			0.328725			0.164363	+	0.986400i	$0.447443\pi$
$74$		−	2.27299e37i		−	0.937483i
$75$	1.04573e37	+	3.52318e36i	0.329758	+	0.111099i
$76$	1.48521e37			0.359349
$77$			2.47199e36i			0.0460503i
$78$	9.78381e36	−	2.90399e37i	0.140804	−	0.417929i
$79$	3.31828e37			0.370145			0.185072	−	0.982725i	$-0.440748\pi$
$79$	3.31828e37			0.370145			0.185072	+	0.982725i	$0.440748\pi$
$80$		−	2.86426e37i		−	0.248435i
$81$	3.95583e37	+	1.42417e38i	0.267631	+	0.963521i
$82$	−2.49738e37			−0.132193
$83$		−	9.06890e37i		−	0.376697i	−0.982102	−	0.188349i	$-0.939686\pi$
$83$		−	9.06890e37i		−	0.376697i	0.982102	−	0.188349i	$-0.0603135\pi$
$84$	−5.16436e36	−	1.73992e36i	−0.0168823	−	0.00568779i
$85$	−5.56862e38			−1.43671
$86$			6.06543e38i			1.23849i
$87$	−1.99424e37	+	5.91921e37i	−0.0323141	+	0.0959132i
$88$	−1.00985e39			−1.30198
$89$		−	1.59950e39i		−	1.64507i	−0.568715	−	0.822535i	$-0.692559\pi$
$89$		−	1.59950e39i		−	1.64507i	0.568715	−	0.822535i	$-0.307441\pi$
$90$	5.68591e38	+	4.32184e38i	0.467681	+	0.355483i
$91$	−3.47888e37			−0.0229410
$92$		−	3.87412e37i		−	0.0205313i
$93$	2.83587e39	+	9.55431e38i	1.21067	+	0.407887i
$94$	1.59280e39			0.549041
$95$			2.20974e39i			0.616410i
$96$	1.19408e39	−	3.54421e39i	0.270152	−	0.801854i
$97$	−3.49860e39			−0.643368			−0.321684	−	0.946847i	$-0.604249\pi$
$97$	−3.49860e39			−0.643368			−0.321684	+	0.946847i	$0.604249\pi$
$98$			4.84991e39i			0.726461i
$99$	6.02267e39	−	7.92356e39i	0.736351	−	0.968761i
$100$	1.63803e39			0.163803
$101$		−	5.95610e39i		−	0.488129i	−0.969759	−	0.244064i	$-0.921519\pi$
$101$		−	5.95610e39i		−	0.488129i	0.969759	−	0.244064i	$-0.0784808\pi$
$102$	1.82275e40	+	6.14102e39i	1.22666	+	0.413273i
$103$	−3.15526e40			−1.74699			−0.873495	−	0.486833i	$-0.838152\pi$
$103$	−3.15526e40			−1.74699			−0.873495	+	0.486833i	$0.838152\pi$
$104$		−	1.42119e40i		−	0.648612i
$105$	2.58871e38	−	7.68369e38i	0.00975657	−	0.0289590i
$106$	−4.38816e40			−1.36825
$107$			7.60315e40i			1.96480i	0.186792	+	0.982399i	$0.440191\pi$
$107$			7.60315e40i			1.96480i	−0.186792	+	0.982399i	$0.559809\pi$
$108$	1.23144e40	+	1.81593e40i	0.264204	+	0.389604i
$109$	−6.31504e40			−1.12680			−0.563399	−	0.826185i	$-0.690507\pi$
$109$	−6.31504e40			−1.12680			−0.563399	+	0.826185i	$0.690507\pi$
$110$		−	4.80903e40i		−	0.714831i
$111$	9.84558e40	+	3.31707e40i	1.22119	+	0.411429i
$112$	1.12315e39			0.0116433
$113$		−	1.27309e41i		−	1.10482i	−0.833574	−	0.552408i	$-0.813709\pi$
$113$		−	1.27309e41i		−	1.10482i	0.833574	−	0.552408i	$-0.186291\pi$
$114$	2.43688e40	−	7.23305e40i	0.177312	−	0.526289i
$115$	5.76403e39			0.0352184
$116$			9.27182e39i			0.0476437i
$117$	1.11510e41	+	8.47581e40i	0.482610	+	0.366829i
$118$	5.92638e40			0.216346
$119$		−	2.18359e40i		−	0.0673337i
$120$	3.13894e41	+	1.05754e41i	0.818762	+	0.275849i
$121$	−2.17566e41			−0.480710
$122$		−	2.47655e41i		−	0.464142i
$123$	3.64453e40	−	1.08175e41i	0.0580149	−	0.172197i
$124$	4.44209e41			0.601387
$125$			9.44092e41i			1.08846i
$126$	−1.69470e40	+	2.22959e40i	−0.0166603	+	0.0219186i
$127$	−1.74320e42			−1.46310			−0.731548	−	0.681790i	$-0.761202\pi$
$127$	−1.74320e42			−1.46310			−0.731548	+	0.681790i	$0.761202\pi$
$128$		−	2.43194e41i		−	0.174483i
$129$	−2.62727e42	−	8.85153e41i	−1.61328	−	0.543531i
$130$	6.76784e41			0.356109
$131$			1.19877e42i			0.541138i	0.962701	+	0.270569i	$0.0872119\pi$
$131$			1.19877e42i			0.541138i	−0.962701	+	0.270569i	$0.912788\pi$
$132$	4.71694e41	−	1.40006e42i	0.182887	−	0.542836i
$133$	−8.66495e40			−0.0288891
$134$			2.12987e42i			0.611303i
$135$	−2.70180e42	+	1.83218e42i	−0.668309	+	0.453203i
$136$	8.92040e42			1.90373
$137$		−	5.40965e42i		−	0.997143i	−0.866848	−	0.498572i	$-0.833858\pi$
$137$		−	5.40965e42i		−	0.997143i	0.866848	−	0.498572i	$-0.166142\pi$
$138$	−1.88671e41	−	6.35651e40i	−0.0300694	−	0.0101306i
$139$	4.69462e42			0.647596			0.323798	−	0.946126i	$-0.395040\pi$
$139$	4.69462e42			0.647596			0.323798	+	0.946126i	$0.395040\pi$
$140$		−	1.20357e41i		−	0.0143850i
$141$	−2.32444e42	+	6.89930e42i	−0.240955	+	0.715193i
$142$	8.07764e42			0.726972
$143$		−	9.43127e42i		−	0.737648i
$144$	−3.60007e42	−	2.73640e42i	−0.244941	−	0.186178i
$145$	−1.37949e42			−0.0817257
$146$		−	4.63153e42i		−	0.239149i
$147$	−2.10077e43	−	7.07768e42i	−0.946305	−	0.318819i
$148$	1.54221e43			0.606609
$149$			3.07904e43i			1.05850i	0.848467	+	0.529248i	$0.177526\pi$
$149$			3.07904e43i			1.05850i	−0.848467	+	0.529248i	$0.822474\pi$
$150$	2.68763e42	−	7.97730e42i	0.0808247	−	0.239900i
$151$	−2.05811e43			−0.541913			−0.270957	−	0.962592i	$-0.587340\pi$
$151$	−2.05811e43			−0.541913			−0.270957	+	0.962592i	$0.587340\pi$
$152$		−	3.53980e43i		−	0.816783i
$153$	−5.32003e43	+	6.99916e43i	−1.07668	+	1.41650i
$154$	1.88574e42			0.0335017
$155$			6.60909e43i			1.03159i
$156$	1.97033e43	+	6.63824e42i	0.270426	+	0.0911090i
$157$	−8.26317e43			−0.998053			−0.499027	−	0.866587i	$-0.666309\pi$
$157$	−8.26317e43			−0.998053			−0.499027	+	0.866587i	$0.666309\pi$
$158$		−	2.53133e43i		−	0.269281i
$159$	6.40382e43	−	1.90075e44i	0.600477	−	1.78231i
$160$	8.25991e43			0.683244
$161$			2.26022e41i			0.00165057i
$162$	1.08642e44	−	3.01767e43i	0.700965	−	0.194703i
$163$	3.73339e43			0.212986			0.106493	−	0.994313i	$-0.466038\pi$
$163$	3.73339e43			0.212986			0.106493	+	0.994313i	$0.466038\pi$
$164$		−	1.69445e43i		−	0.0855368i
$165$	2.08306e44	+	7.01801e43i	0.931155	+	0.313715i
$166$	−6.91814e43			−0.274049
$167$		−	1.57442e43i		−	0.0553085i	−0.999618	−	0.0276542i	$-0.991196\pi$
$167$		−	1.57442e43i		−	0.0553085i	0.999618	−	0.0276542i	$-0.00880374\pi$
$168$	−4.14686e42	+	1.23085e43i	−0.0129281	+	0.0383726i
$169$	−2.28461e44			−0.632524
$170$			4.24798e44i			1.04521i
$171$	2.77741e44	+	2.11110e44i	0.607740	+	0.461941i
$172$	−4.11535e44			−0.801379
$173$		−	8.54435e44i		−	1.48169i	−0.671677	−	0.740844i	$-0.734426\pi$
$173$		−	8.54435e44i		−	1.48169i	0.671677	−	0.740844i	$-0.265574\pi$
$174$	4.51542e43	+	1.52129e43i	0.0697772	+	0.0235086i
$175$	−9.55654e42			−0.0131686
$176$			3.04486e44i			0.374381i
$177$	−8.64861e43	+	2.56704e44i	−0.0949470	+	0.281817i
$178$	−1.22017e45			−1.19679
$179$		−	7.02562e44i		−	0.616061i	−0.951376	−	0.308031i	$-0.900330\pi$
$179$		−	7.02562e44i		−	0.616061i	0.951376	−	0.308031i	$-0.0996699\pi$
$180$	−2.93234e44	+	3.85785e44i	−0.230019	+	0.302618i
$181$	−1.07815e45			−0.757023			−0.378512	−	0.925597i	$-0.623564\pi$
$181$	−1.07815e45			−0.757023			−0.378512	+	0.925597i	$0.623564\pi$
$182$			2.65384e43i			0.0166896i
$183$	1.07273e45	+	3.61413e44i	0.604601	+	0.203696i
$184$	−9.23342e43			−0.0466666
$185$			2.29454e45i			1.04055i
$186$	7.28843e44	−	2.16332e45i	0.296739	−	0.880769i
$187$	5.91974e45			2.16506
$188$			1.08070e45i			0.355263i
$189$	−7.18443e43	−	1.05944e44i	−0.0212401	−	0.0313214i
$190$	1.68569e45			0.448441
$191$		−	6.61122e45i		−	1.58349i	−0.610854	−	0.791744i	$-0.709174\pi$
$191$		−	6.61122e45i		−	1.58349i	0.610854	−	0.791744i	$-0.290826\pi$
$192$	−4.05499e45	−	1.36617e45i	−0.874914	−	0.294767i
$193$	2.19460e45			0.426785			0.213393	−	0.976967i	$-0.431549\pi$
$193$	2.19460e45			0.426785			0.213393	+	0.976967i	$0.431549\pi$
$194$			2.66888e45i			0.468052i
$195$	−9.87658e44	+	2.93152e45i	−0.156284	+	0.463875i
$196$	−3.29063e45			−0.470065
$197$			6.74413e45i			0.870165i	0.900391	+	0.435082i	$0.143281\pi$
$197$			6.74413e45i			0.870165i	−0.900391	+	0.435082i	$0.856719\pi$
$198$	−6.04443e45	−	4.59434e45i	−0.704777	−	0.535698i
$199$	8.11167e45			0.855163			0.427581	−	0.903977i	$-0.359366\pi$
$199$	8.11167e45			0.855163			0.427581	+	0.903977i	$0.359366\pi$
$200$		−	3.90403e45i		−	0.372317i
$201$	−9.22563e45	−	3.10820e45i	−0.796297	−	0.268280i
$202$	−4.54356e45			−0.355115
$203$		−	5.40932e43i		−	0.00383021i
$204$	−4.16664e45	+	1.23672e46i	−0.267413	+	0.793723i
$205$	2.52106e45			0.146726
$206$			2.40696e46i			1.27094i
$207$	5.50671e44	−	7.24476e44i	0.0263928	−	0.0347230i
$208$	−4.28509e45			−0.186506
$209$		−	2.34908e46i		−	0.928905i
$210$	−5.86145e44	−	1.97478e44i	−0.0210678	−	0.00709794i
$211$	−8.13952e45			−0.266042			−0.133021	−	0.991113i	$-0.542468\pi$
$211$	−8.13952e45			−0.266042			−0.133021	+	0.991113i	$0.542468\pi$
$212$		−	2.97733e46i		−	0.885340i
$213$	−1.17880e46	+	3.49887e46i	−0.319043	+	0.946970i
$214$	5.80001e46			1.42940
$215$		−	6.12295e46i		−	1.37465i
$216$	4.32802e46	−	2.93498e46i	0.885552	−	0.600523i
$217$	−2.59159e45			−0.0483471
$218$			4.81738e46i			0.819749i
$219$	2.00617e46	+	6.75899e45i	0.311520	+	0.104954i
$220$	3.26289e46			0.462540
$221$			8.33097e46i			1.07857i
$222$	2.53040e46	−	7.51063e46i	0.299316	−	0.888417i
$223$	−1.06382e47			−1.15020			−0.575099	−	0.818084i	$-0.695037\pi$
$223$	−1.06382e47			−1.15020			−0.575099	+	0.818084i	$0.695037\pi$
$224$			3.23891e45i			0.0320213i
$225$	3.06319e46	+	2.32832e46i	0.277028	+	0.210568i
$226$	−9.71167e46			−0.803758
$227$			8.34023e46i			0.631918i	0.948773	+	0.315959i	$0.102326\pi$
$227$			8.34023e46i			0.631918i	−0.948773	+	0.315959i	$0.897674\pi$
$228$	4.90757e46	+	1.65341e46i	0.340541	+	0.114732i
$229$	−2.48520e47			−1.57998			−0.789991	−	0.613118i	$-0.789915\pi$
$229$	−2.48520e47			−1.57998			−0.789991	+	0.613118i	$0.789915\pi$
$230$		−	4.39705e45i		−	0.0256215i
$231$	−2.75194e45	+	8.16817e45i	−0.0147028	+	0.0436401i
$232$	2.20981e46			0.108292
$233$		−	2.13690e47i		−	0.960874i	−0.877029	−	0.480437i	$-0.840478\pi$
$233$		−	2.13690e47i		−	0.960874i	0.877029	−	0.480437i	$-0.159522\pi$
$234$	6.46571e46	−	8.50644e46i	0.266870	−	0.351100i
$235$	−1.60791e47			−0.609401
$236$			4.02101e46i			0.139989i
$237$	1.09646e47	+	3.69407e46i	0.350772	+	0.118178i
$238$	−1.66574e46			−0.0489855
$239$			2.29981e47i			0.621919i	0.950423	+	0.310960i	$0.100650\pi$
$239$			2.29981e47i			0.621919i	−0.950423	+	0.310960i	$0.899350\pi$
$240$	3.18863e46	−	9.46435e46i	0.0793194	−	0.235432i
$241$	4.94933e47			1.13294			0.566468	−	0.824084i	$-0.308309\pi$
$241$	4.94933e47			1.13294			0.566468	+	0.824084i	$0.308309\pi$
$242$			1.65968e47i			0.349718i
$243$	−2.78331e46	+	5.14625e47i	−0.0540053	+	0.998541i
$244$	1.68032e47			0.300328
$245$		−	4.89590e47i		−	0.806327i
$246$	−8.25207e46	−	2.78020e46i	−0.125274	−	0.0422060i
$247$	3.30590e47			0.462755
$248$		−	1.05871e48i		−	1.36692i
$249$	1.00959e47	−	2.99663e47i	0.120271	−	0.356982i
$250$	7.20193e47			0.791861
$251$			2.52858e47i			0.256686i	0.991730	+	0.128343i	$0.0409658\pi$
$251$			2.52858e47i			0.256686i	−0.991730	+	0.128343i	$0.959034\pi$
$252$	−1.51276e46	−	1.14984e46i	−0.0141827	−	0.0107802i
$253$	−6.12747e46			−0.0530727
$254$			1.32979e48i			1.06441i
$255$	−1.84003e48	−	6.19925e47i	−1.36152	−	0.458707i
$256$	−1.53483e48			−1.05017
$257$		−	9.03481e47i		−	0.571816i	−0.958257	−	0.285908i	$-0.907705\pi$
$257$		−	9.03481e47i		−	0.571816i	0.958257	−	0.285908i	$-0.0922952\pi$
$258$	−6.75232e47	+	2.00420e48i	−0.395420	+	1.17367i
$259$	−8.99748e46			−0.0487669
$260$			4.59193e47i			0.230424i
$261$	−1.31791e47	+	1.73387e47i	−0.0612456	+	0.0805762i
$262$	9.14469e47			0.393680
$263$			2.34262e48i			0.934515i	0.884121	+	0.467258i	$0.154758\pi$
$263$			2.34262e48i			0.934515i	−0.884121	+	0.467258i	$0.845242\pi$
$264$	−3.33686e48	−	1.12422e48i	−1.23384	−	0.415692i
$265$	4.42977e48			1.51867
$266$			6.60999e46i			0.0210169i
$267$	1.78064e48	−	5.28522e48i	0.525232	−	1.55897i
$268$	−1.44510e48			−0.395550
$269$			1.32049e48i			0.335498i	0.985830	+	0.167749i	$0.0536497\pi$
$269$			1.32049e48i			0.335498i	−0.985830	+	0.167749i	$0.946350\pi$
$270$	1.39766e48	+	2.06104e48i	0.329707	+	0.486197i
$271$	2.36177e48			0.517431			0.258715	−	0.965954i	$-0.416701\pi$
$271$	2.36177e48			0.517431			0.258715	+	0.965954i	$0.416701\pi$
$272$		−	2.68963e48i		−	0.547412i
$273$	−1.14952e47	−	3.87285e46i	−0.0217403	−	0.00732450i
$274$	−4.12671e48			−0.725425
$275$		−	2.59079e48i		−	0.423426i
$276$	4.31285e46	−	1.28012e47i	0.00655515	−	0.0194567i
$277$	5.44564e48			0.769934			0.384967	−	0.922930i	$-0.374213\pi$
$277$	5.44564e48			0.769934			0.384967	+	0.922930i	$0.374213\pi$
$278$		−	3.58126e48i		−	0.471128i
$279$	8.30691e48	+	6.31405e48i	1.01708	+	0.773079i
$280$	−2.86855e47			−0.0326965
$281$		−	2.36324e48i		−	0.250831i	−0.992104	−	0.125415i	$-0.959974\pi$
$281$		−	2.36324e48i		−	0.250831i	0.992104	−	0.125415i	$-0.0400264\pi$
$282$	5.26308e48	+	1.77318e48i	0.520305	+	0.175296i
$283$	−7.13943e48			−0.657559			−0.328780	−	0.944407i	$-0.606637\pi$
$283$	−7.13943e48			−0.657559			−0.328780	+	0.944407i	$0.606637\pi$
$284$			5.48062e48i			0.470395i
$285$	−2.45999e48	+	7.30164e48i	−0.196805	+	0.584149i
$286$	−7.19457e48			−0.536642
$287$			9.88571e46i			0.00687654i
$288$	7.89117e48	−	1.03818e49i	0.512026	−	0.673633i
$289$	−3.57731e49			−2.16571
$290$			1.05233e48i			0.0594557i
$291$	−1.15604e49	−	3.89481e48i	−0.609695	−	0.205412i
$292$	3.14246e48			0.154744
$293$			2.22736e49i			1.02432i	0.858889	+	0.512162i	$0.171155\pi$
$293$			2.22736e49i			1.02432i	−0.858889	+	0.512162i	$0.828845\pi$
$294$	−5.39915e48	+	1.60255e49i	−0.231942	+	0.688440i
$295$	−5.98258e48			−0.240131
$296$		−	3.67564e49i		−	1.37879i
$297$	2.87215e49	−	1.94770e49i	1.00711	−	0.682958i
$298$	2.34882e49			0.770060
$299$		−	8.62331e47i		−	0.0264393i
$300$	5.41254e48	+	1.82354e48i	0.155230	+	0.0522985i
$301$	2.40096e48			0.0644251
$302$			1.57001e49i			0.394244i
$303$	6.63061e48	−	1.96807e49i	0.155848	−	0.462581i
$304$	−1.06730e49			−0.234863
$305$			2.50003e49i			0.515168i
$306$	5.33925e49	+	4.05834e49i	1.03051	+	0.783286i
$307$	5.70004e49			1.03065			0.515324	−	0.856995i	$-0.327672\pi$
$307$	5.70004e49			1.03065			0.515324	+	0.856995i	$0.327672\pi$
$308$			1.27946e48i			0.0216777i
$309$	−1.04259e50	−	3.51258e49i	−1.65556	−	0.557772i
$310$	5.04169e49			0.750486
$311$		−	7.28213e48i		−	0.101637i	−0.998708	−	0.0508183i	$-0.983817\pi$
$311$		−	7.28213e48i		−	0.101637i	0.998708	−	0.0508183i	$-0.0161829\pi$
$312$	1.58213e49	−	4.69602e49i	0.207086	−	0.614665i
$313$	−3.78599e49			−0.464829			−0.232414	−	0.972617i	$-0.574663\pi$
$313$	−3.78599e49			−0.464829			−0.232414	+	0.972617i	$0.574663\pi$
$314$			6.30350e49i			0.726087i
$315$	1.71077e48	−	2.25073e48i	0.0184919	−	0.0243283i
$316$	1.71749e49			0.174242
$317$		−	1.33083e50i		−	1.26747i	−0.773551	−	0.633734i	$-0.781521\pi$
$317$		−	1.33083e50i		−	1.26747i	0.773551	−	0.633734i	$-0.218479\pi$
$318$	−1.44998e50	−	4.88510e49i	−1.29664	−	0.436849i
$319$	1.46647e49			0.123157
$320$		−	9.45030e49i		−	0.745497i
$321$	−8.46419e49	+	2.51230e50i	−0.627313	+	1.86196i
$322$	1.72419e47			0.00120079
$323$			2.07502e50i			1.35823i
$324$	2.04747e49	+	7.37126e49i	0.125985	+	0.453567i
$325$	3.64606e49			0.210939
$326$		−	2.84799e49i		−	0.154948i
$327$	−2.08667e50	−	7.03020e49i	−1.06782	−	0.359760i
$328$	−4.03850e49			−0.194421
$329$		−	6.30499e48i		−	0.0285606i
$330$	5.35364e49	−	1.58904e50i	0.228229	−	0.677418i
$331$	9.02089e49			0.361984			0.180992	−	0.983485i	$-0.442069\pi$
$331$	9.02089e49			0.361984			0.180992	+	0.983485i	$0.442069\pi$
$332$		−	4.69391e49i		−	0.177326i
$333$	2.88400e50	+	2.19211e50i	1.02591	+	0.779791i
$334$	−1.20104e49			−0.0402371
$335$		−	2.15006e50i		−	0.678508i
$336$	3.71121e48	+	1.25034e48i	0.0110339	+	0.00371743i
$337$	4.88792e50			1.36939			0.684694	−	0.728831i	$-0.259936\pi$
$337$	4.88792e50			1.36939			0.684694	+	0.728831i	$0.259936\pi$
$338$			1.74279e50i			0.460163i
$339$	1.41726e50	−	4.20666e50i	0.352742	−	1.04699i
$340$	−2.88222e50			−0.676315
$341$		−	7.02581e50i		−	1.55456i
$342$	1.61044e50	−	2.11873e50i	0.336063	−	0.442133i
$343$	3.84236e49			0.0756338
$344$			9.80838e50i			1.82150i
$345$	1.90460e49	+	6.41679e48i	0.0333751	+	0.0112444i
$346$	−6.51799e50			−1.07793
$347$			6.91641e50i			1.07967i	0.841770	+	0.539836i	$0.181514\pi$
$347$			6.91641e50i			1.07967i	−0.841770	+	0.539836i	$0.818486\pi$
$348$	−1.03218e49	+	3.06368e49i	−0.0152115	+	0.0451501i
$349$	2.54661e50			0.354368			0.177184	−	0.984178i	$-0.443301\pi$
$349$	2.54661e50			0.354368			0.177184	+	0.984178i	$0.443301\pi$
$350$			7.29013e48i			0.00958020i
$351$	2.74104e50	+	4.04204e50i	0.340231	+	0.501716i
$352$	−8.78072e50			−1.02962
$353$		−	2.97692e50i		−	0.329817i	−0.986309	−	0.164908i	$-0.947267\pi$
$353$		−	2.97692e50i		−	0.329817i	0.986309	−	0.164908i	$-0.0527328\pi$
$354$	1.95825e50	+	6.59753e49i	0.205023	+	0.0690742i
$355$	−8.15424e50			−0.806894
$356$		−	8.27875e50i		−	0.774399i
$357$	2.43088e49	−	7.21523e49i	0.0214981	−	0.0638096i
$358$	−5.35944e50			−0.448186
$359$		−	7.16053e50i		−	0.566312i	−0.959074	−	0.283156i	$-0.908619\pi$
$359$		−	7.16053e50i		−	0.566312i	0.959074	−	0.283156i	$-0.0913815\pi$
$360$	9.19466e50	+	6.98882e50i	0.687837	+	0.522822i
$361$	−5.89595e50			−0.417263
$362$			8.22461e50i			0.550737i
$363$	−7.18901e50	−	2.42205e50i	−0.455551	−	0.153479i
$364$	−1.80061e49			−0.0107992
$365$			4.67545e50i			0.265440i
$366$	2.75701e50	−	8.18325e50i	0.148189	−	0.439849i
$367$	7.07406e48			0.00360037			0.00180019	−	0.999998i	$-0.499427\pi$
$367$	7.07406e48			0.00360037			0.00180019	+	0.999998i	$0.499427\pi$
$368$			2.78401e49i			0.0134188i
$369$	2.40852e50	−	3.16870e50i	0.109957	−	0.144662i
$370$	1.75038e51			0.757002
$371$			1.73702e50i			0.0711749i
$372$	1.46780e51	+	4.94515e50i	0.569911	+	0.192009i
$373$	3.50408e51			1.28943			0.644715	−	0.764423i	$-0.276976\pi$
$373$	3.50408e51			1.28943			0.644715	+	0.764423i	$0.276976\pi$
$374$		−	4.51583e51i		−	1.57509i
$375$	−1.05101e51	+	3.11956e51i	−0.347521	+	1.03150i
$376$	2.57571e51			0.807496
$377$			2.06379e50i			0.0613535i
$378$	−8.08186e49	+	5.48059e49i	−0.0227864	+	0.0154522i
$379$	2.66002e51			0.711380			0.355690	−	0.934604i	$-0.384246\pi$
$379$	2.66002e51			0.711380			0.355690	+	0.934604i	$0.384246\pi$
$380$			1.14373e51i			0.290168i
$381$	−5.76004e51	−	1.94061e51i	−1.38652	−	0.467132i
$382$	−5.04332e51			−1.15199
$383$			5.50035e51i			1.19238i	0.802843	+	0.596190i	$0.203320\pi$
$383$			5.50035e51i			1.19238i	−0.802843	+	0.596190i	$0.796680\pi$
$384$	2.70735e50	−	8.03584e50i	0.0557083	−	0.165351i
$385$	−1.90362e50			−0.0371848
$386$		−	1.67413e51i		−	0.310487i
$387$	−7.69588e51	−	5.84961e51i	−1.35531	−	1.03017i
$388$	−1.81082e51			−0.302859
$389$		−	1.68466e51i		−	0.267621i	−0.991007	−	0.133811i	$-0.957279\pi$
$389$		−	1.68466e51i		−	0.267621i	0.991007	−	0.133811i	$-0.0427214\pi$
$390$	2.23629e51	+	7.53428e50i	0.337471	+	0.113697i
$391$	5.41261e50			0.0776017
$392$			7.84277e51i			1.06844i
$393$	−1.33452e51	+	3.96107e51i	−0.172773	+	0.512816i
$394$	5.14471e51			0.633048
$395$			2.55533e51i			0.298886i
$396$	3.11723e51	−	4.10110e51i	0.346629	−	0.456033i
$397$	−3.30787e51			−0.349735			−0.174867	−	0.984592i	$-0.555950\pi$
$397$	−3.30787e51			−0.349735			−0.174867	+	0.984592i	$0.555950\pi$
$398$		−	6.18793e51i		−	0.622134i
$399$	−2.86315e50	−	9.64623e49i	−0.0273771	−	0.00922359i
$400$	−1.17712e51			−0.107059
$401$			6.54095e51i			0.565918i	0.959132	+	0.282959i	$0.0913161\pi$
$401$			6.54095e51i			0.565918i	−0.959132	+	0.282959i	$0.908684\pi$
$402$	−2.37107e51	+	7.03770e51i	−0.195174	+	0.579308i
$403$	9.88756e51			0.774441
$404$		−	3.08278e51i		−	0.229781i
$405$	−1.09672e52	+	3.04629e51i	−0.778028	+	0.216108i
$406$	−4.12646e49			−0.00278649
$407$		−	2.43922e52i		−	1.56806i
$408$	2.94756e52	+	9.93061e51i	1.80409	+	0.607817i
$409$	1.03181e52			0.601361			0.300681	−	0.953725i	$-0.402786\pi$
$409$	1.03181e52			0.601361			0.300681	+	0.953725i	$0.402786\pi$
$410$		−	1.92317e51i		−	0.106743i
$411$	6.02227e51	−	1.78751e52i	0.318364	−	0.944955i
$412$	−1.63311e52			−0.822376
$413$		−	2.34592e50i		−	0.0112541i
$414$	−5.52661e50	−	4.20076e50i	−0.0252611	−	0.0192009i
$415$	6.98374e51			0.304177
$416$		−	1.23573e52i		−	0.512928i
$417$	1.55124e52	+	5.22627e51i	0.613702	+	0.206762i
$418$	−1.79197e52			−0.675781
$419$			2.41773e52i			0.869216i	0.900620	+	0.434608i	$0.143113\pi$
$419$			2.41773e52i			0.869216i	−0.900620	+	0.434608i	$0.856887\pi$
$420$	1.33987e50	−	3.97695e50i	0.00459280	−	0.0136321i
$421$	−9.16325e51			−0.299508			−0.149754	−	0.988723i	$-0.547848\pi$
$421$	−9.16325e51			−0.299508			−0.149754	+	0.988723i	$0.547848\pi$
$422$			6.20917e51i			0.193546i
$423$	−1.53613e52	+	2.02096e52i	−0.456688	+	0.600829i
$424$	−7.09607e52			−2.01234
$425$			2.28853e52i			0.619125i
$426$	2.66909e52	+	8.99241e51i	0.688924	+	0.232105i
$427$	−9.80325e50			−0.0241442
$428$			3.93526e52i			0.924908i
$429$	1.04993e52	−	3.11637e52i	0.235514	−	0.699041i
$430$	−4.67084e52			−1.00006
$431$		−	4.88658e52i		−	0.998756i	−0.866384	−	0.499378i	$-0.833562\pi$
$431$		−	4.88658e52i		−	0.998756i	0.866384	−	0.499378i	$-0.166438\pi$
$432$	−8.84939e51	−	1.30496e52i	−0.172678	−	0.254638i
$433$	8.00000e52			1.49050			0.745250	−	0.666785i	$-0.232330\pi$
$433$	8.00000e52			1.49050			0.745250	+	0.666785i	$0.232330\pi$
$434$			1.97697e51i			0.0351727i
$435$	−4.55824e51	−	1.53571e51i	−0.0774483	−	0.0260931i
$436$	−3.26856e52			−0.530428
$437$		−	2.14783e51i		−	0.0332945i
$438$	5.15604e51	−	1.53039e52i	0.0763544	−	0.226632i
$439$	3.21396e52			0.454727			0.227363	−	0.973810i	$-0.426989\pi$
$439$	3.21396e52			0.454727			0.227363	+	0.973810i	$0.426989\pi$
$440$		−	7.77665e52i		−	1.05133i
$441$	−6.15362e52	−	4.67734e52i	−0.794985	−	0.604265i
$442$	6.35521e52			0.784666
$443$			8.40809e52i			0.992254i	0.868250	+	0.496127i	$0.165245\pi$
$443$			8.40809e52i			0.992254i	−0.868250	+	0.496127i	$0.834755\pi$
$444$	5.09590e52	+	1.71686e52i	0.574860	+	0.193676i
$445$	1.23174e53			1.32837
$446$			8.11531e52i			0.836773i
$447$	−3.42773e52	+	1.01740e53i	−0.337953	+	1.00310i
$448$	3.70569e51			0.0349389
$449$		−	8.23425e52i		−	0.742502i	−0.928533	−	0.371251i	$-0.878929\pi$
$449$		−	8.23425e52i		−	0.742502i	0.928533	−	0.371251i	$-0.121071\pi$
$450$	1.77614e52	−	2.33673e52i	0.153189	−	0.201539i
$451$	−2.68002e52			−0.221110
$452$		−	6.58930e52i		−	0.520080i
$453$	−6.80060e52	−	2.29119e52i	−0.513551	−	0.173020i
$454$	6.36228e52			0.459722
$455$		−	2.67900e51i		−	0.0185244i
$456$	3.94067e52	−	1.16965e53i	0.260779	−	0.774034i
$457$	7.33005e52			0.464283			0.232142	−	0.972682i	$-0.425427\pi$
$457$	7.33005e52			0.464283			0.232142	+	0.972682i	$0.425427\pi$
$458$			1.89582e53i			1.14944i
$459$	−2.53707e53	+	1.72047e53i	−1.47258	+	0.998607i
$460$	2.98336e51			0.0165787
$461$		−	2.57982e53i		−	1.37269i	−0.727278	−	0.686343i	$-0.759215\pi$
$461$		−	2.57982e53i		−	1.37269i	0.727278	−	0.686343i	$-0.240785\pi$
$462$	6.23103e51	+	2.09929e51i	0.0317483	+	0.0106963i
$463$	−1.75519e53			−0.856456			−0.428228	−	0.903671i	$-0.640862\pi$
$463$	−1.75519e53			−0.856456			−0.428228	+	0.903671i	$0.640862\pi$
$464$		−	6.66291e51i		−	0.0311390i
$465$	−7.35755e52	+	2.18383e53i	−0.329362	+	0.977599i
$466$	−1.63012e53			−0.699039
$467$		−	3.11819e53i		−	1.28105i	−0.767938	−	0.640524i	$-0.778717\pi$
$467$		−	3.11819e53i		−	1.28105i	0.767938	−	0.640524i	$-0.221283\pi$
$468$	5.77156e52	+	4.38694e52i	0.227183	+	0.172681i
$469$	8.43093e51			0.0317994
$470$			1.22658e53i			0.443341i
$471$	−2.73039e53	−	9.19895e52i	−0.945817	−	0.318655i
$472$	9.58352e52			0.318189
$473$			6.50902e53i			2.07154i
$474$	2.81799e52	−	8.36424e52i	0.0859751	−	0.255188i
$475$	9.08136e52			0.265631
$476$		−	1.13019e52i		−	0.0316966i
$477$	4.23202e53	−	5.56774e53i	1.13810	−	1.49731i
$478$	1.75439e53			0.452448
$479$			2.86386e53i			0.708339i	0.935181	+	0.354170i	$0.115236\pi$
$479$			2.86386e53i			0.708339i	−0.935181	+	0.354170i	$0.884764\pi$
$480$	2.72932e53	+	9.19532e52i	0.647484	+	0.218143i
$481$	3.43277e53			0.781165
$482$		−	3.77556e53i		−	0.824215i
$483$	−2.51618e50	+	7.46842e50i	−0.000526986	+	0.00156418i
$484$	−1.12608e53			−0.226289
$485$		−	2.69419e53i		−	0.519509i
$486$	3.92578e53	+	2.12323e52i	0.726442	+	0.0392890i
$487$	−5.81411e53			−1.03253			−0.516266	−	0.856428i	$-0.672679\pi$
$487$	−5.81411e53			−1.03253			−0.516266	+	0.856428i	$0.672679\pi$
$488$		−	4.00482e53i		−	0.682631i
$489$	1.23362e53	+	4.15618e52i	0.201839	+	0.0680013i
$490$	−3.73480e53			−0.586605
$491$			5.05390e53i			0.762073i	0.924560	+	0.381037i	$0.124433\pi$
$491$			5.05390e53i			0.762073i	−0.924560	+	0.381037i	$0.875567\pi$
$492$	1.88635e52	−	5.59897e52i	0.0273099	−	0.0810599i
$493$	−1.29539e53			−0.180078
$494$		−	2.52188e53i		−	0.336655i
$495$	6.10175e53	+	4.63791e53i	0.782258	+	0.594591i
$496$	−3.19217e53			−0.393055
$497$		−	3.19748e52i		−	0.0378164i
$498$	−2.28596e53	−	7.70160e52i	−0.259705	−	0.0874972i
$499$	−8.14125e53			−0.888547			−0.444273	−	0.895891i	$-0.646538\pi$
$499$	−8.14125e53			−0.888547			−0.444273	+	0.895891i	$0.646538\pi$
$500$			4.88646e53i			0.512382i
$501$	1.75272e52	−	5.20235e52i	0.0176587	−	0.0524137i
$502$	1.92891e53			0.186740
$503$		−	2.55895e53i		−	0.238069i	−0.992890	−	0.119035i	$-0.962020\pi$
$503$		−	2.55895e53i		−	0.238069i	0.992890	−	0.119035i	$-0.0379799\pi$
$504$	−2.74049e52	+	3.60545e52i	−0.0245029	+	0.0322366i
$505$	4.58665e53			0.394156
$506$			4.67429e52i			0.0386105i
$507$	−7.54900e53	−	2.54333e53i	−0.599419	−	0.201950i
$508$	−9.02251e53			−0.688736
$509$			5.38650e53i			0.395322i	0.980270	+	0.197661i	$0.0633345\pi$
$509$			5.38650e53i			0.395322i	−0.980270	+	0.197661i	$0.936665\pi$
$510$	−4.72905e53	+	1.40366e54i	−0.333711	+	0.990507i
$511$	−1.83336e52			−0.0124403
$512$			9.03437e53i			0.589520i
$513$	6.82720e53	+	1.00676e54i	0.428445	+	0.631800i
$514$	−6.89214e53			−0.415998
$515$		−	2.42979e54i		−	1.41067i
$516$	−1.35983e54	−	4.58140e53i	−0.759436	−	0.255861i
$517$	1.70929e54			0.918343
$518$			6.86366e52i			0.0354781i
$519$	9.51197e53	−	2.82330e54i	0.473068	−	1.40414i
$520$	1.09442e54			0.523743
$521$		−	3.14146e54i		−	1.44670i	−0.690483	−	0.723349i	$-0.742602\pi$
$521$		−	3.14146e54i		−	1.44670i	0.690483	−	0.723349i	$-0.257398\pi$
$522$	1.32267e53	+	1.00536e53i	0.0586194	+	0.0445564i
$523$	2.68713e54			1.14619			0.573093	−	0.819490i	$-0.305743\pi$
$523$	2.68713e54			1.14619			0.573093	+	0.819490i	$0.305743\pi$
$524$			6.20461e53i			0.254735i
$525$	−3.15776e52	−	1.06388e52i	−0.0124794	−	0.00420442i
$526$	1.78705e54			0.679863
$527$			6.20614e54i			2.27305i
$528$	−3.38968e53	+	1.00611e54i	−0.119531	+	0.354787i
$529$	2.93959e54			0.998098
$530$		−	3.37922e54i		−	1.10484i
$531$	−5.71551e53	+	7.51946e53i	−0.179955	+	0.236753i
$532$	−4.48483e52			−0.0135992
$533$		−	3.77165e53i		−	0.110151i
$534$	−4.03179e54	−	1.35835e54i	−1.13416	−	0.382108i
$535$	−5.85501e54			−1.58654
$536$			3.44420e54i			0.899067i
$537$	7.82125e53	−	2.32147e54i	0.196694	−	0.583818i
$538$	1.00733e54			0.244076
$539$			5.20461e54i			1.21510i
$540$	−1.39840e54	+	9.48305e53i	−0.314599	+	0.213340i
$541$	−4.82090e53			−0.104516			−0.0522581	−	0.998634i	$-0.516642\pi$
$541$	−4.82090e53			−0.104516			−0.0522581	+	0.998634i	$0.516642\pi$
$542$		−	1.80166e54i		−	0.376433i
$543$	−3.56253e54	−	1.20025e54i	−0.717402	−	0.241699i
$544$	7.75632e54			1.50549
$545$		−	4.86306e54i		−	0.909871i
$546$	−2.95438e52	+	8.76905e52i	−0.00532860	+	0.0158161i
$547$	−1.01012e55			−1.75641			−0.878203	−	0.478287i	$-0.841258\pi$
$547$	−1.01012e55			−1.75641			−0.878203	+	0.478287i	$0.841258\pi$
$548$		−	2.79994e54i		−	0.469394i
$549$	3.14227e54	+	2.38843e54i	0.507922	+	0.386069i
$550$	−1.97636e54			−0.308044
$551$			5.14036e53i			0.0772612i
$552$	−3.05099e53	−	1.02791e53i	−0.0442242	−	0.0148995i
$553$	−1.00201e53			−0.0140078
$554$		−	4.15417e54i		−	0.560130i
$555$	−2.55440e54	+	7.58185e54i	−0.332222	+	0.986087i
$556$	2.42986e54			0.304849
$557$			7.16935e54i			0.867712i	0.900982	+	0.433856i	$0.142847\pi$
$557$			7.16935e54i			0.867712i	−0.900982	+	0.433856i	$0.857153\pi$
$558$	4.81662e54	−	6.33686e54i	0.562417	−	0.739929i
$559$	−9.16027e54			−1.03198
$560$			8.64909e52i			0.00940177i
$561$	1.95606e55	+	6.59013e54i	2.05175	+	0.691253i
$562$	−1.80278e54			−0.182480
$563$		−	9.44183e54i		−	0.922334i	−0.887313	−	0.461167i	$-0.847431\pi$
$563$		−	9.44183e54i		−	0.922334i	0.887313	−	0.461167i	$-0.152569\pi$
$564$	−1.20309e54	+	3.57096e54i	−0.113427	+	0.336669i
$565$	9.80376e54			0.892121
$566$			5.44626e54i			0.478376i
$567$	−1.19453e53	−	4.30051e53i	−0.0101282	−	0.0364635i
$568$	1.30623e55			1.06919
$569$		−	8.75930e54i		−	0.692188i	−0.938200	−	0.346094i	$-0.887508\pi$
$569$		−	8.75930e54i		−	0.692188i	0.938200	−	0.346094i	$-0.112492\pi$
$570$	5.57000e54	+	1.87659e54i	0.424970	+	0.143176i
$571$	−1.49462e55			−1.10105			−0.550527	−	0.834817i	$-0.685573\pi$
$571$	−1.49462e55			−1.10105			−0.550527	+	0.834817i	$0.685573\pi$
$572$		−	4.88146e54i		−	0.347240i
$573$	7.35993e54	−	2.18454e55i	0.505570	−	1.50061i
$574$	7.54124e52			0.00500270
$575$		−	2.36884e53i		−	0.0151767i
$576$	−1.18780e55	−	9.02842e54i	−0.735011	−	0.558679i
$577$	−7.67058e54			−0.458471			−0.229235	−	0.973371i	$-0.573623\pi$
$577$	−7.67058e54			−0.458471			−0.229235	+	0.973371i	$0.573623\pi$
$578$			2.72893e55i			1.57556i
$579$	7.25160e54	+	2.44313e54i	0.404448	+	0.136262i
$580$	−7.14001e53			−0.0384715
$581$			2.73850e53i			0.0142557i
$582$	−2.97112e54	+	8.81876e54i	−0.149438	+	0.443555i
$583$	−4.70908e55			−2.28857
$584$		−	7.48963e54i		−	0.351725i
$585$	−6.52702e54	+	8.58711e54i	−0.296209	+	0.389699i
$586$	1.69912e55			0.745199
$587$			1.94666e55i			0.825142i	0.910925	+	0.412571i	$0.135369\pi$
$587$			1.94666e55i			0.825142i	−0.910925	+	0.412571i	$0.864631\pi$
$588$	−1.08732e55	−	3.66329e54i	−0.445462	−	0.150081i
$589$	2.46273e55			0.975237
$590$			4.56377e54i			0.174696i
$591$	−7.50789e54	+	2.22846e55i	−0.277823	+	0.824622i
$592$	−1.10826e55			−0.396467
$593$		−	3.28169e55i		−	1.13502i	−0.823366	−	0.567511i	$-0.807906\pi$
$593$		−	3.28169e55i		−	1.13502i	0.823366	−	0.567511i	$-0.192094\pi$
$594$	−1.48579e55	−	2.19100e55i	−0.496854	−	0.732679i
$595$	1.68153e54			0.0543709
$596$			1.59366e55i			0.498276i
$597$	2.68033e55	+	9.03029e54i	0.810405	+	0.273033i
$598$	−6.57823e53			−0.0192347
$599$			1.31443e55i			0.371706i	0.982578	+	0.185853i	$0.0595049\pi$
$599$			1.31443e55i			0.371706i	−0.982578	+	0.185853i	$0.940495\pi$
$600$	4.34615e54	−	1.29000e55i	0.118872	−	0.352831i
$601$	5.12314e55			1.35534			0.677668	−	0.735368i	$-0.262991\pi$
$601$	5.12314e55			1.35534			0.677668	+	0.735368i	$0.262991\pi$
$602$		−	1.83155e54i		−	0.0468694i
$603$	−2.70240e55	−	2.05408e55i	−0.668964	−	0.508477i
$604$	−1.06524e55			−0.255100
$605$		−	1.67542e55i		−	0.388165i
$606$	−1.50133e55	−	5.05811e54i	−0.336529	−	0.113380i
$607$	4.17916e55			0.906390			0.453195	−	0.891411i	$-0.350284\pi$
$607$	4.17916e55			0.906390			0.453195	+	0.891411i	$0.350284\pi$
$608$		−	3.07787e55i		−	0.645919i
$609$	6.02191e52	−	1.78740e53i	0.00122289	−	0.00362974i
$610$	1.90713e55			0.374787
$611$			2.40552e55i			0.457493i
$612$	−2.75356e55	+	3.62264e55i	−0.506834	+	0.666803i
$613$	5.19647e55			0.925762			0.462881	−	0.886420i	$-0.346816\pi$
$613$	5.19647e55			0.925762			0.462881	+	0.886420i	$0.346816\pi$
$614$		−	4.34823e55i		−	0.749800i
$615$	8.33033e54	+	2.80657e54i	0.139046	+	0.0468460i
$616$	3.04942e54			0.0492723
$617$		−	6.97080e55i		−	1.09038i	−0.838311	−	0.545192i	$-0.816457\pi$
$617$		−	6.97080e55i		−	1.09038i	0.838311	−	0.545192i	$-0.183543\pi$
$618$	−2.67955e55	+	7.95331e55i	−0.405781	+	1.20442i
$619$	2.92695e55			0.429144			0.214572	−	0.976708i	$-0.431164\pi$
$619$	2.92695e55			0.429144			0.214572	+	0.976708i	$0.431164\pi$
$620$			3.42075e55i			0.485610i
$621$	2.62610e54	−	1.78085e54i	0.0360977	−	0.0244791i
$622$	−5.55511e54			−0.0739410
$623$			4.82995e54i			0.0622560i
$624$	−1.41592e55	−	4.77037e54i	−0.176745	−	0.0595470i
$625$	−4.39188e55			−0.530946
$626$			2.88812e55i			0.338164i
$627$	2.61510e55	−	7.76203e55i	0.296577	−	0.880288i
$628$	−4.27688e55			−0.469823
$629$			2.15465e56i			2.29279i
$630$	−1.71695e54	−	1.30505e54i	−0.0176989	−	0.0134529i
$631$	−1.07837e56			−1.07691			−0.538456	−	0.842653i	$-0.680992\pi$
$631$	−1.07837e56			−1.07691			−0.538456	+	0.842653i	$0.680992\pi$
$632$		−	4.09339e55i		−	0.396043i
$633$	−2.68954e55	−	9.06130e54i	−0.252118	−	0.0849408i
$634$	−1.01521e56			−0.922088
$635$		−	1.34240e56i		−	1.18143i
$636$	3.31451e55	−	9.83798e55i	0.282668	−	0.839003i
$637$	−7.32454e55			−0.605330
$638$		−	1.11869e55i		−	0.0895973i
$639$	−7.79022e55	+	1.02490e56i	−0.604690	+	0.795544i
$640$	1.87278e55			0.140892
$641$			7.67846e55i			0.559904i	0.960014	+	0.279952i	$0.0903185\pi$
$641$			7.67846e55i			0.559904i	−0.960014	+	0.279952i	$0.909682\pi$
$642$	1.91649e56	+	6.45684e55i	1.35459	+	0.456373i
$643$	−2.77175e55			−0.189904			−0.0949521	−	0.995482i	$-0.530270\pi$
$643$	−2.77175e55			−0.189904			−0.0949521	+	0.995482i	$0.530270\pi$
$644$			1.16985e53i			0.000776986i
$645$	6.81635e55	−	2.02320e56i	0.438892	−	1.30270i
$646$	1.58291e56			0.988113
$647$			4.92799e55i			0.298253i	0.988818	+	0.149126i	$0.0476461\pi$
$647$			4.92799e55i			0.298253i	−0.988818	+	0.149126i	$0.952354\pi$
$648$	1.75684e56	−	4.87987e55i	1.03094	−	0.286357i
$649$	6.35980e55			0.361867
$650$		−	2.78137e55i		−	0.153459i
$651$	−8.56336e54	−	2.88508e54i	−0.0458167	−	0.0154361i
$652$	1.93234e55			0.100261
$653$		−	4.82221e55i		−	0.242651i	−0.992613	−	0.121326i	$-0.961286\pi$
$653$		−	4.82221e55i		−	0.242651i	0.992613	−	0.121326i	$-0.0387145\pi$
$654$	−5.36294e55	+	1.59180e56i	−0.261726	+	0.776845i
$655$	−9.23141e55			−0.436960
$656$			1.21767e55i			0.0559051i
$657$	5.87654e55	+	4.46673e55i	0.261706	+	0.198922i
$658$	−4.80972e54			−0.0207779
$659$		−	5.78616e55i		−	0.242483i	−0.992623	−	0.121242i	$-0.961312\pi$
$659$		−	5.78616e55i		−	0.242483i	0.992623	−	0.121242i	$-0.0386876\pi$
$660$	1.07815e56	+	3.63240e55i	0.438331	+	0.147678i
$661$	1.33081e55			0.0524913			0.0262457	−	0.999656i	$-0.491645\pi$
$661$	1.33081e55			0.0524913			0.0262457	+	0.999656i	$0.491645\pi$
$662$		−	6.88151e55i		−	0.263345i
$663$	−9.27442e55	+	2.75279e56i	−0.344363	+	1.02212i
$664$	−1.11873e56			−0.403054
$665$		−	6.67267e54i		−	0.0233274i
$666$	1.67224e56	−	2.20003e56i	0.567300	−	0.746354i
$667$	1.34084e54			0.00441429
$668$		−	8.14894e54i		−	0.0260359i
$669$	−3.51519e56	−	1.18430e56i	−1.09000	−	0.367231i
$670$	−1.64016e56			−0.493617
$671$		−	2.65767e56i		−	0.776338i
$672$	−3.60571e54	+	1.07023e55i	−0.0102236	+	0.0303454i
$673$	1.47294e56			0.405400			0.202700	−	0.979241i	$-0.435028\pi$
$673$	1.47294e56			0.405400			0.202700	+	0.979241i	$0.435028\pi$
$674$		−	3.72872e56i		−	0.996234i
$675$	7.52969e55	+	1.11035e56i	0.195300	+	0.287996i
$676$	−1.18247e56			−0.297754
$677$			3.30872e56i			0.808885i	0.914563	+	0.404442i	$0.132534\pi$
$677$			3.30872e56i			0.808885i	−0.914563	+	0.404442i	$0.867466\pi$
$678$	−3.20902e56	−	1.08115e56i	−0.761691	−	0.256621i
$679$	1.05646e55			0.0243476
$680$			6.86939e56i			1.53723i
$681$	−9.28474e55	+	2.75586e56i	−0.201756	+	0.598845i
$682$	−5.35959e56			−1.13095
$683$			5.51189e56i			1.12950i	0.825262	+	0.564751i	$0.191028\pi$
$683$			5.51189e56i			1.12950i	−0.825262	+	0.564751i	$0.808972\pi$
$684$	1.43754e56	+	1.09267e56i	0.286087	+	0.217453i
$685$	4.16584e56			0.805177
$686$		−	2.93112e55i		−	0.0550238i
$687$	−8.21184e56	−	2.76665e56i	−1.49729	−	0.504451i
$688$	2.95737e56			0.523765
$689$		−	6.62718e56i		−	1.14010i
$690$	4.89500e54	−	1.45291e55i	0.00818033	−	0.0242805i
$691$	9.50175e56			1.54256			0.771281	−	0.636495i	$-0.219616\pi$
$691$	9.50175e56			1.54256			0.771281	+	0.636495i	$0.219616\pi$
$692$		−	4.42241e56i		−	0.697488i
$693$	−1.81864e55	+	2.39265e55i	−0.0278665	+	0.0366618i
$694$	5.27613e56			0.785464
$695$			3.61521e56i			0.522923i
$696$	7.30186e55	+	2.46007e55i	0.102624	+	0.0345750i
$697$	2.36736e56			0.323302
$698$		−	1.94267e56i		−	0.257804i
$699$	2.37890e56	−	7.06095e56i	0.306784	−	0.910584i
$700$	−4.94630e54			−0.00619897
$701$		−	8.19263e56i		−	0.997844i	−0.866647	−	0.498922i	$-0.833729\pi$
$701$		−	8.19263e56i		−	0.997844i	0.866647	−	0.498922i	$-0.166271\pi$
$702$	3.08344e56	−	2.09098e56i	0.365000	−	0.247519i
$703$	8.55010e56			0.983705
$704$			1.00462e57i			1.12343i
$705$	−5.31299e56	−	1.79000e56i	−0.577506	−	0.194567i
$706$	−2.27092e56			−0.239943
$707$			1.79854e55i			0.0184727i
$708$	−4.47637e55	+	1.32866e56i	−0.0446952	+	0.132662i
$709$	−4.46538e56			−0.433445			−0.216722	−	0.976233i	$-0.569537\pi$
$709$	−4.46538e56			−0.433445			−0.216722	+	0.976233i	$0.569537\pi$
$710$			6.22040e56i			0.587018i
$711$	3.21177e56	+	2.44126e56i	0.294682	+	0.223986i
$712$	−1.97313e57			−1.76017
$713$		−	6.42392e55i		−	0.0557198i
$714$	−5.50408e55	−	1.85438e55i	−0.0464217	−	0.0156399i
$715$	7.26280e56			0.595639
$716$		−	3.63634e56i		−	0.290004i
$717$	−2.56026e56	+	7.59924e56i	−0.198564	+	0.589369i
$718$	−5.46235e56			−0.411994
$719$			3.53173e56i			0.259066i	0.991575	+	0.129533i	$0.0413478\pi$
$719$			3.53173e56i			0.259066i	−0.991575	+	0.129533i	$0.958652\pi$
$720$	2.10723e56	−	2.77233e56i	0.150336	−	0.197785i
$721$	9.52780e55			0.0661131
$722$			4.49768e56i			0.303560i
$723$	1.63540e57	+	5.50983e56i	1.07364	+	0.361720i
$724$	−5.58034e56			−0.356360
$725$			5.66928e55i			0.0352182i
$726$	−1.84764e56	+	5.48408e56i	−0.111657	+	0.331414i
$727$	−2.39148e57			−1.40598			−0.702988	−	0.711202i	$-0.748151\pi$
$727$	−2.39148e57			−1.40598			−0.702988	+	0.711202i	$0.748151\pi$
$728$			4.29150e55i			0.0245461i
$729$	−6.64874e56	+	1.66949e57i	−0.369989	+	0.929036i
$730$	3.56663e56			0.193109
$731$		−	5.74964e57i		−	3.02896i
$732$	5.55227e56	+	1.87061e56i	0.284609	+	0.0958876i
$733$	−2.68497e57			−1.33924			−0.669621	−	0.742703i	$-0.733544\pi$
$733$	−2.68497e57			−1.33924			−0.669621	+	0.742703i	$0.733544\pi$
$734$		−	5.39639e54i		−	0.00261928i
$735$	5.45035e56	−	1.61775e57i	0.257441	−	0.764125i
$736$	−8.02849e55			−0.0369044
$737$			2.28563e57i			1.02248i
$738$	−2.41722e56	−	1.83732e56i	−0.105242	−	0.0799940i
$739$	3.96152e57			1.67870			0.839350	−	0.543592i	$-0.182936\pi$
$739$	3.96152e57			1.67870			0.839350	+	0.543592i	$0.182936\pi$
$740$			1.18762e57i			0.489826i
$741$	1.09237e57	+	3.68028e56i	0.438535	+	0.147747i
$742$	1.32507e56			0.0517800
$743$			5.20343e57i			1.97931i	0.143480	+	0.989653i	$0.454171\pi$
$743$			5.20343e57i			1.97931i	−0.143480	+	0.989653i	$0.545829\pi$
$744$	1.17861e57	−	3.49829e57i	0.436426	−	1.29538i
$745$	−2.37109e57			−0.854719
$746$		−	2.67306e57i		−	0.938064i
$747$	6.67198e56	−	8.77781e56i	0.227952	−	0.299898i
$748$	3.06396e57			1.01918
$749$		−	2.29589e56i		−	0.0743558i
$750$	2.37973e57	+	8.01753e56i	0.750416	+	0.252822i
$751$	2.58539e57			0.793831			0.396916	−	0.917855i	$-0.370081\pi$
$751$	2.58539e57			0.793831			0.396916	+	0.917855i	$0.370081\pi$
$752$		−	7.76615e56i		−	0.232193i
$753$	−2.81493e56	+	8.35517e56i	−0.0819537	+	0.243252i
$754$	1.57435e56			0.0446349
$755$		−	1.58490e57i		−	0.437586i
$756$	−3.71854e55	−	5.48349e55i	−0.00999853	−	0.0147442i
$757$	−5.70991e57			−1.49524			−0.747621	−	0.664125i	$-0.768804\pi$
$757$	−5.70991e57			−1.49524			−0.747621	+	0.664125i	$0.768804\pi$
$758$		−	2.02918e57i		−	0.517531i
$759$	−2.02470e56	−	6.82139e55i	−0.0502949	−	0.0169448i
$760$	2.72592e57			0.659539
$761$			8.23286e57i			1.94025i	0.242606	+	0.970125i	$0.421998\pi$
$761$			8.23286e57i			1.94025i	−0.242606	+	0.970125i	$0.578002\pi$
$762$	−1.48038e57	+	4.39400e57i	−0.339840	+	1.00870i
$763$	1.90693e56			0.0426426
$764$		−	3.42186e57i		−	0.745409i
$765$	−5.38988e57	−	4.09683e57i	−1.14380	−	0.869399i
$766$	4.19590e57			0.867461
$767$			8.95027e56i			0.180272i
$768$	−5.07152e57	−	1.70864e57i	−0.995208	−	0.335295i
$769$	−8.76098e57			−1.67504			−0.837522	−	0.546404i	$-0.815996\pi$
$769$	−8.76098e57			−1.67504			−0.837522	+	0.546404i	$0.815996\pi$
$770$			1.45216e56i			0.0270521i
$771$	1.00580e57	−	2.98536e57i	0.182567	−	0.541888i
$772$	1.13589e57			0.200904
$773$		−	4.08303e57i		−	0.703708i	−0.936055	−	0.351854i	$-0.885551\pi$
$773$		−	4.08303e57i		−	0.703708i	0.936055	−	0.351854i	$-0.114449\pi$
$774$	−4.46233e57	+	5.87075e57i	−0.749450	+	0.985994i
$775$	2.71613e57			0.444546
$776$			4.31583e57i			0.688383i
$777$	−2.97303e56	−	1.00164e56i	−0.0462146	−	0.0155701i
$778$	−1.28513e57			−0.194695
$779$		−	9.39416e56i		−	0.138710i
$780$	−5.11195e56	+	1.51731e57i	−0.0735690	+	0.218364i
$781$	8.66839e57			1.21596
$782$		−	4.12897e56i		−	0.0564555i
$783$	−6.28498e56	+	4.26206e56i	−0.0837662	+	0.0568047i
$784$	2.36471e57			0.307225
$785$		−	6.36327e57i		−	0.805912i
$786$	3.02167e57	+	1.01803e57i	0.373075	+	0.125693i
$787$	4.26039e57			0.512807			0.256404	−	0.966570i	$-0.417462\pi$
$787$	4.26039e57			0.512807			0.256404	+	0.966570i	$0.417462\pi$
$788$			3.49065e57i			0.409621i
$789$	−2.60791e57	+	7.74069e57i	−0.298368	+	0.885604i
$790$	1.94931e57			0.217440
$791$			3.84430e56i			0.0418107i
$792$	−9.77441e57	−	7.42949e57i	−1.03654	−	0.787872i
$793$	3.74019e57			0.386750
$794$			2.52339e57i			0.254433i
$795$	1.46373e58	+	4.93143e57i	1.43919	+	0.484875i
$796$	4.19846e57			0.402558
$797$		−	5.36913e57i		−	0.502039i	−0.967982	−	0.251019i	$-0.919234\pi$
$797$		−	5.36913e57i		−	0.502039i	0.967982	−	0.251019i	$-0.0807658\pi$
$798$	−7.35856e55	+	2.18414e56i	−0.00671019	+	0.0199169i
$799$	−1.50987e58			−1.34278
$800$		−	3.39457e57i		−	0.294432i
$801$	1.17675e58	−	1.54816e58i	0.995484	−	1.30968i
$802$	4.98972e57			0.411707
$803$		−	4.97026e57i		−	0.400007i
$804$	−4.77503e57	−	1.60875e57i	−0.374848	−	0.126290i
$805$	−1.74054e55			−0.00133280
$806$		−	7.54265e57i		−	0.563408i
$807$	−1.47003e57	+	4.36328e57i	−0.107116	+	0.317938i
$808$	−7.34737e57			−0.522282
$809$			1.38188e58i			0.958299i	0.877733	+	0.479149i	$0.159055\pi$
$809$			1.38188e58i			0.958299i	−0.877733	+	0.479149i	$0.840945\pi$
$810$	2.32384e57	+	8.36624e57i	0.157219	+	0.566018i
$811$	1.63622e58			1.08001			0.540003	−	0.841663i	$-0.318423\pi$
$811$	1.63622e58			1.08001			0.540003	+	0.841663i	$0.318423\pi$
$812$		−	2.79977e55i		−	0.00180303i
$813$	7.80399e57	+	2.62924e57i	0.490349	+	0.165203i
$814$	−1.86074e58			−1.14077
$815$			2.87499e57i			0.171983i
$816$	2.99422e57	−	8.88733e57i	0.174776	−	0.518762i
$817$	−2.28158e58			−1.29955
$818$		−	7.87112e57i		−	0.437492i
$819$	−3.36722e56	−	2.55941e56i	−0.0182639	−	0.0138823i
$820$	1.30486e57			0.0690695
$821$			2.83310e58i			1.46352i	0.681561	+	0.731761i	$0.261301\pi$
$821$			2.83310e58i			1.46352i	−0.681561	+	0.731761i	$0.738699\pi$
$822$	−1.36359e58	−	4.59405e57i	−0.687458	−	0.231611i
$823$	−2.86770e58			−1.41103			−0.705516	−	0.708694i	$-0.749285\pi$
$823$	−2.86770e58			−1.41103			−0.705516	+	0.708694i	$0.749285\pi$
$824$			3.89229e58i			1.86922i
$825$	2.88418e57	−	8.56071e57i	0.135190	−	0.401265i
$826$	−1.78957e56			−0.00818741
$827$			3.40026e57i			0.151846i	0.997114	+	0.0759229i	$0.0241903\pi$
$827$			3.40026e57i			0.151846i	−0.997114	+	0.0759229i	$0.975810\pi$
$828$	2.85018e56	−	3.74977e56i	0.0124241	−	0.0163455i
$829$	2.96641e57			0.126224			0.0631118	−	0.998006i	$-0.479898\pi$
$829$	2.96641e57			0.126224			0.0631118	+	0.998006i	$0.479898\pi$
$830$		−	5.32750e57i		−	0.221290i
$831$	1.79940e58	+	6.06234e57i	0.729637	+	0.245822i
$832$	−1.41382e58			−0.559663
$833$		−	4.59741e58i		−	1.77670i
$834$	3.98682e57	−	1.18335e58i	0.150420	−	0.446470i
$835$	1.21242e57			0.0446607
$836$		−	1.21584e58i		−	0.437272i
$837$	2.04194e58	+	3.01111e58i	0.717023	+	1.05735i
$838$	1.84435e58			0.632357
$839$		−	3.96022e58i		−	1.32581i	−0.748705	−	0.662903i	$-0.769324\pi$
$839$		−	3.96022e58i		−	1.32581i	0.748705	−	0.662903i	$-0.230676\pi$
$840$	−9.47851e56	−	3.19340e56i	−0.0309852	−	0.0104392i
$841$	3.10062e58			0.989756
$842$			6.99012e57i			0.217893i
$843$	2.63087e57	−	7.80882e57i	0.0800843	−	0.237703i
$844$	−4.21288e57			−0.125236
$845$		−	1.75932e58i		−	0.510753i
$846$	1.54168e58	+	1.17182e58i	0.437105	+	0.332242i
$847$	6.56974e56			0.0181920
$848$			2.13957e58i			0.578641i
$849$	−2.35908e58	−	7.94795e57i	−0.623144	−	0.209943i
$850$	1.74579e58			0.450415
$851$		−	2.23026e57i		−	0.0562036i
$852$	−6.10129e57	+	1.81096e58i	−0.150186	+	0.445776i
$853$	−3.49792e58			−0.841064			−0.420532	−	0.907278i	$-0.638157\pi$
$853$	−3.49792e58			−0.841064			−0.420532	+	0.907278i	$0.638157\pi$
$854$			7.47834e56i			0.0175650i
$855$	−1.62571e58	+	2.13882e58i	−0.373009	+	0.490740i
$856$	9.37916e58			2.10227
$857$			5.19481e58i			1.13750i	0.822509	+	0.568752i	$0.192574\pi$
$857$			5.19481e58i			1.13750i	−0.822509	+	0.568752i	$0.807426\pi$
$858$	−2.37730e58	−	8.00934e57i	−0.508555	−	0.171337i
$859$	−4.54785e57			−0.0950480			−0.0475240	−	0.998870i	$-0.515133\pi$
$859$	−4.54785e57			−0.0950480			−0.0475240	+	0.998870i	$0.515133\pi$
$860$		−	3.16913e58i		−	0.647100i
$861$	−1.10052e56	+	3.26653e56i	−0.00219551	+	0.00651663i
$862$	−3.72769e58			−0.726598
$863$			5.80750e58i			1.10605i	0.833166	+	0.553023i	$0.186526\pi$
$863$			5.80750e58i			1.10605i	−0.833166	+	0.553023i	$0.813474\pi$
$864$	3.76323e58	−	2.55197e58i	0.700302	−	0.474899i
$865$	6.57980e58			1.19644
$866$		−	6.10274e58i		−	1.08434i
$867$	−1.18205e59	−	3.98243e58i	−2.05236	−	0.691459i
$868$	−1.34136e57			−0.0227589
$869$		−	2.71645e58i		−	0.450408i
$870$	−1.17151e57	+	3.47722e57i	−0.0189828	+	0.0563439i
$871$	−3.21661e58			−0.509373
$872$			7.79016e58i			1.20564i
$873$	−3.38630e58	−	2.57392e58i	−0.512202	−	0.389322i
$874$	−1.63846e57			−0.0242218
$875$		−	2.85084e57i		−	0.0411918i
$876$	1.03836e58	+	3.49834e57i	0.146645	+	0.0494060i
$877$	−8.40716e58			−1.16053			−0.580266	−	0.814427i	$-0.697052\pi$
$877$	−8.40716e58			−1.16053			−0.580266	+	0.814427i	$0.697052\pi$
$878$		−	2.45175e58i		−	0.330815i
$879$	−2.47960e58	+	7.35983e58i	−0.327042	+	0.970712i
$880$	−2.34477e58			−0.302307
$881$		−	4.01495e57i		−	0.0506014i	−0.999680	−	0.0253007i	$-0.991946\pi$
$881$		−	4.01495e57i		−	0.0506014i	0.999680	−	0.0253007i	$-0.00805432\pi$
$882$	−3.56808e58	+	4.69424e58i	−0.439605	+	0.578354i
$883$	6.53581e58			0.787200			0.393600	−	0.919282i	$-0.371229\pi$
$883$	6.53581e58			0.787200			0.393600	+	0.919282i	$0.371229\pi$
$884$			4.31197e58i			0.507727i
$885$	−1.97682e58	−	6.66009e57i	−0.227563	−	0.0766681i
$886$	6.41405e58			0.721868
$887$			4.06535e58i			0.447327i	0.974666	+	0.223664i	$0.0718017\pi$
$887$			4.06535e58i			0.447327i	−0.974666	+	0.223664i	$0.928198\pi$
$888$	4.09190e58	−	1.21454e59i	0.440216	−	1.30663i
$889$	5.26387e57			0.0553694
$890$		−	9.39622e58i		−	0.966391i
$891$	1.16587e59	−	3.23837e58i	1.17246	−	0.325666i
$892$	−5.50618e58			−0.541443
$893$			5.99149e58i			0.576111i
$894$	7.76119e58	+	2.61482e58i	0.729756	+	0.245862i
$895$	5.41026e58			0.497459
$896$			7.34363e56i			0.00660314i
$897$	9.59987e56	−	2.84939e57i	0.00844144	−	0.0250555i
$898$	−6.28144e58			−0.540172
$899$			1.53742e58i			0.129300i
$900$	1.58546e58	+	1.20510e58i	0.130408	+	0.0991226i
$901$	4.15969e59			3.34631
$902$			2.04444e58i			0.160858i
$903$	7.93347e57	+	2.67286e57i	0.0610532	+	0.0205694i
$904$	−1.57047e59			−1.18212
$905$		−	8.30261e58i		−	0.611284i
$906$	−1.74781e58	+	5.18779e58i	−0.125873	+	0.373610i
$907$	−2.71841e59			−1.91500			−0.957502	−	0.288425i	$-0.906868\pi$
$907$	−2.71841e59			−1.91500			−0.957502	+	0.288425i	$0.906868\pi$
$908$			4.31676e58i			0.297469i
$909$	4.38189e58	−	5.76492e58i	0.295382	−	0.388612i
$910$	−2.04366e57			−0.0134766
$911$		−	2.28820e59i		−	1.47613i	−0.674728	−	0.738067i	$-0.735739\pi$
$911$		−	2.28820e59i		−	1.47613i	0.674728	−	0.738067i	$-0.264261\pi$
$912$	−3.52668e58	−	1.18817e58i	−0.222571	−	0.0749863i
$913$	−7.42409e58			−0.458382
$914$		−	5.59167e58i		−	0.337767i
$915$	−2.78316e58	+	8.26084e58i	−0.164481	+	0.488205i
$916$	−1.28630e59			−0.743759
$917$		−	3.61986e57i		−	0.0204788i
$918$	1.31245e59	+	1.93539e59i	0.726490	+	1.07131i
$919$	−2.71886e58			−0.147257			−0.0736286	−	0.997286i	$-0.523458\pi$
$919$	−2.71886e58			−0.147257			−0.0736286	+	0.997286i	$0.523458\pi$
$920$		−	7.11044e57i		−	0.0376825i
$921$	1.88346e59	+	6.34555e58i	0.976706	+	0.329061i
$922$	−1.96800e59			−0.998633
$923$			1.21992e59i			0.605755i
$924$	−1.42435e57	+	4.22771e57i	−0.00692116	+	0.0205431i
$925$	9.42987e58			0.448405
$926$			1.33894e59i			0.623074i
$927$	−3.05398e59	−	2.32132e59i	−1.39082	−	1.05716i
$928$	1.92144e58			0.0856381
$929$			4.64079e58i			0.202431i	0.994865	+	0.101216i	$0.0322732\pi$
$929$			4.64079e58i			0.202431i	−0.994865	+	0.101216i	$0.967727\pi$
$930$	1.66592e59	+	5.61265e58i	0.711206	+	0.239612i
$931$	−1.82435e59			−0.762279
$932$		−	1.10603e59i		−	0.452321i
$933$	8.10681e57	−	2.40623e58i	0.0324502	−	0.0963172i
$934$	−2.37869e59			−0.931967
$935$			4.55865e59i			1.74825i
$936$	1.04557e59	−	1.37557e59i	0.392496	−	0.516376i
$937$	2.92671e59			1.07544			0.537722	−	0.843122i	$-0.319285\pi$
$937$	2.92671e59			1.07544			0.537722	+	0.843122i	$0.319285\pi$
$938$		−	6.43147e57i		−	0.0231341i
$939$	−1.25100e59	−	4.21475e58i	−0.440500	−	0.148409i
$940$	−8.32225e58			−0.286869
$941$		−	4.95833e59i		−	1.67318i	−0.547830	−	0.836590i	$-0.684546\pi$
$941$		−	4.95833e59i		−	1.67318i	0.547830	−	0.836590i	$-0.315454\pi$
$942$	−7.01735e58	+	2.08286e59i	−0.231822	+	0.688085i
$943$	−2.45043e57			−0.00792517
$944$		−	2.88957e58i		−	0.0914942i
$945$	8.15850e57	−	5.53256e57i	0.0252915	−	0.0171510i
$946$	4.96536e59			1.50705
$947$			4.00119e59i			1.18902i	0.804088	+	0.594511i	$0.202654\pi$
$947$			4.00119e59i			1.18902i	−0.804088	+	0.594511i	$0.797346\pi$
$948$	5.67508e58	+	1.91199e58i	0.165122	+	0.0556312i
$949$	6.99474e58			0.199272
$950$		−	6.92765e58i		−	0.193247i
$951$	1.48154e59	−	4.39745e59i	0.404673	−	1.20113i
$952$	−2.69366e58			−0.0720449
$953$		−	2.68151e59i		−	0.702298i	−0.936320	−	0.351149i	$-0.885791\pi$
$953$		−	2.68151e59i		−	0.702298i	0.936320	−	0.351149i	$-0.114209\pi$
$954$	−4.24731e59	−	3.22836e59i	−1.08930	−	0.827970i
$955$	5.09115e59			1.27864
$956$			1.19034e59i			0.292762i
$957$	4.84565e58	+	1.63255e58i	0.116711	+	0.0393212i
$958$	2.18467e59			0.515319
$959$			1.63353e58i			0.0377359i
$960$	1.05205e59	−	3.12265e59i	0.238019	−	0.706479i
$961$	2.85270e59			0.632103
$962$		−	2.61866e59i		−	0.568300i
$963$	−5.59363e59	+	7.35911e59i	−1.18896	+	1.56423i
$964$	2.56169e59			0.533317
$965$			1.69001e59i			0.344622i
$966$	5.69723e56	+	1.91945e56i	0.00113794	+	0.000383384i
$967$	−1.84962e59			−0.361871			−0.180935	−	0.983495i	$-0.557912\pi$
$967$	−1.84962e59			−0.361871			−0.180935	+	0.983495i	$0.557912\pi$
$968$			2.68387e59i			0.514344i
$969$	−2.31001e59	+	6.85647e59i	−0.433649	+	1.28714i
$970$	−2.05524e59			−0.377945
$971$		−	6.01927e59i		−	1.08433i	−0.840274	−	0.542163i	$-0.817606\pi$
$971$		−	6.01927e59i		−	1.08433i	0.840274	−	0.542163i	$-0.182394\pi$
$972$	−1.44060e58	+	2.66361e59i	−0.0254224	+	0.470052i
$973$	−1.41761e58			−0.0245076
$974$			4.43525e59i			0.751171i
$975$	1.20477e59	+	4.05897e58i	0.199899	+	0.0673478i
$976$	−1.20751e59			−0.196288
$977$			2.20249e59i			0.350771i	0.984500	+	0.175385i	$0.0561172\pi$
$977$			2.20249e59i			0.350771i	−0.984500	+	0.175385i	$0.943883\pi$
$978$	3.17051e58	−	9.41058e58i	0.0494712	−	0.146838i
$979$	−1.30940e60			−2.00179
$980$		−	2.53404e59i		−	0.379570i
$981$	−6.11234e59	−	4.64597e59i	−0.897073	−	0.681861i
$982$	3.85533e59			0.554411
$983$		−	2.85145e59i		−	0.401787i	−0.979613	−	0.200893i	$-0.935616\pi$
$983$		−	2.85145e59i		−	0.401787i	0.979613	−	0.200893i	$-0.0643844\pi$
$984$	−1.33444e59	−	4.49585e58i	−0.184245	−	0.0620740i
$985$	−5.19349e59			−0.702644
$986$			9.88175e58i			0.131007i
$987$	7.01902e57	−	2.08335e58i	0.00911871	−	0.0270658i
$988$	1.71108e59			0.217837
$989$			5.95140e58i			0.0742495i
$990$	3.53800e59	−	4.65467e59i	0.432567	−	0.569095i
$991$	1.38819e60			1.66332			0.831662	−	0.555282i	$-0.187390\pi$
$991$	1.38819e60			1.66332			0.831662	+	0.555282i	$0.187390\pi$
$992$		−	9.20554e59i		−	1.08098i
$993$	2.98076e59	+	1.00425e59i	0.343038	+	0.115573i
$994$	−2.43917e58			−0.0275115
$995$			6.24660e59i			0.690530i
$996$	5.22548e58	−	1.55100e59i	0.0566160	−	0.168045i
$997$	−1.42404e60			−1.51224			−0.756119	−	0.654434i	$-0.772907\pi$
$997$	−1.42404e60			−1.51224			−0.756119	+	0.654434i	$0.772907\pi$
$998$			6.21049e59i			0.646421i
$999$	7.08920e59	+	1.04540e60i	0.723248	+	1.06653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.41.b.a.2.4	✓	12
3.2	odd	2	inner	3.41.b.a.2.9	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.41.b.a.2.4	✓	12	1.1	even	1	trivial
3.41.b.a.2.9	yes	12	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 41 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-762842. i q^{2} +(3.30429e9 + 1.11325e9i) q^{3} +5.17583e11 q^{4} +7.70076e13i q^{5} +(8.49232e14 - 2.52065e15i) q^{6} -3.01966e15 q^{7} -1.23359e18i q^{8} +(9.67903e18 + 7.35699e18i) q^{9} +O(q^{10})\)	\(q-762842. i q^{2} +(3.30429e9 + 1.11325e9i) q^{3} +5.17583e11 q^{4} +7.70076e13i q^{5} +(8.49232e14 - 2.52065e15i) q^{6} -3.01966e15 q^{7} -1.23359e18i q^{8} +(9.67903e18 + 7.35699e18i) q^{9} +5.87447e19 q^{10} -8.18632e20i q^{11} +(1.71025e21 + 5.76198e20i) q^{12} +1.15208e22 q^{13} +2.30352e21i q^{14} +(-8.57285e22 + 2.54456e23i) q^{15} -3.71945e23 q^{16} +7.23126e24i q^{17} +(5.61222e24 - 7.38357e24i) q^{18} +2.86951e25 q^{19} +3.98578e25i q^{20} +(-9.97783e24 - 3.36163e24i) q^{21} -6.24487e26 q^{22} -7.48501e25i q^{23} +(1.37329e27 - 4.07614e27i) q^{24} +3.16477e27 q^{25} -8.78853e27i q^{26} +(2.37922e28 + 3.50848e28i) q^{27} -1.56292e27 q^{28} +1.79137e28i q^{29} +(1.94110e29 + 6.53973e28i) q^{30} +8.58238e29 q^{31} -1.07261e30i q^{32} +(9.11340e29 - 2.70500e30i) q^{33} +5.51631e30 q^{34} -2.32537e29i q^{35} +(5.00970e30 + 3.80785e30i) q^{36} +2.97963e31 q^{37} -2.18899e31i q^{38} +(3.80680e31 + 1.28255e31i) q^{39} +9.49957e31 q^{40} -3.27378e31i q^{41} +(-2.56439e30 + 7.61152e30i) q^{42} -7.95109e32 q^{43} -4.23710e32i q^{44} +(-5.66544e32 + 7.45359e32i) q^{45} -5.70989e31 q^{46} +2.08798e33i q^{47} +(-1.22902e33 - 4.14067e32i) q^{48} -6.35769e33 q^{49} -2.41422e33i q^{50} +(-8.05018e33 + 2.38942e34i) q^{51} +5.96295e33 q^{52} -5.75238e34i q^{53} +(2.67642e34 - 1.81497e34i) q^{54} +6.30409e34 q^{55} +3.72502e33i q^{56} +(9.48171e34 + 3.19448e34i) q^{57} +1.36653e34 q^{58} +7.76882e34i q^{59} +(-4.43716e34 + 1.31702e35i) q^{60} +3.24648e35 q^{61} -6.54700e35i q^{62} +(-2.92274e34 - 2.22156e34i) q^{63} -1.22719e36 q^{64} +8.87187e35i q^{65} +(-2.06349e36 - 6.95209e35i) q^{66} -2.79201e36 q^{67} +3.74278e36i q^{68} +(8.33267e34 - 2.47327e35i) q^{69} -1.77389e35 q^{70} +1.05889e37i q^{71} +(9.07549e36 - 1.19399e37i) q^{72} +6.07142e36 q^{73} -2.27299e37i q^{74} +(1.04573e37 + 3.52318e36i) q^{75} +1.48521e37 q^{76} +2.47199e36i q^{77} +(9.78381e36 - 2.90399e37i) q^{78} +3.31828e37 q^{79} -2.86426e37i q^{80} +(3.95583e37 + 1.42417e38i) q^{81} -2.49738e37 q^{82} -9.06890e37i q^{83} +(-5.16436e36 - 1.73992e36i) q^{84} -5.56862e38 q^{85} +6.06543e38i q^{86} +(-1.99424e37 + 5.91921e37i) q^{87} -1.00985e39 q^{88} -1.59950e39i q^{89} +(5.68591e38 + 4.32184e38i) q^{90} -3.47888e37 q^{91} -3.87412e37i q^{92} +(2.83587e39 + 9.55431e38i) q^{93} +1.59280e39 q^{94} +2.20974e39i q^{95} +(1.19408e39 - 3.54421e39i) q^{96} -3.49860e39 q^{97} +4.84991e39i q^{98} +(6.02267e39 - 7.92356e39i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots - 23\!\cdots\!20 q^{9}+O(q^{10}) \) 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9	\( 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots + 54\!\cdots\!80 q^{99}+O(q^{100}) \) 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9 - 129384136354706290080 * q^10 - 4708039830028985428272 * q^12 + 704368845864154901976 * q^13 + 320935800901459838631840 * q^15 + 6054431850962872672227456 * q^16 + 10227710367381761273509920 * q^18 + 37616619688417835612151720 * q^19 - 179163719456723608834234728 * q^21 + 846315150249292772829325920 * q^22 - 18213480358094369517645250944 * q^24 + 8842265325510151276196474700 * q^25 - 70717074113738779393083858252 * q^27 + 469404222007499612173589889696 * q^28 - 207809636542026559976510503200 * q^30 - 914600368399753689553849145016 * q^31 + 157344642221562801276041757600 * q^33 - 14575908480758621487300381842304 * q^34 + 41100171486790863962401658870544 * q^36 + 5673106137824212681873457220696 * q^37 - 9206461430638842876438079090008 * q^39 + 50495897877443363581635475618560 * q^40 - 939238658319640212873301303645920 * q^42 + 1012654832326802922602871229857576 * q^43 + 196109968512215856818385626472000 * q^45 - 3082500781506234684371181468390336 * q^46 + 6532128822166367998693520969705088 * q^48 + 8498166150175390075155260408801892 * q^49 + 27565453699222767413826960590504832 * q^51 - 57328509042562386918101767400001504 * q^52 - 102847607224782098537542351912875792 * q^54 - 9637639495259752880102706884884800 * q^55 - 40307213604482059940636368892395464 * q^57 + 772129436848561910287203884295052320 * q^58 - 114385571579949295944121547557720320 * q^60 - 494443282701607071691140418439862696 * q^61 + 1379291076525018665154441723571240776 * q^63 - 6231783699524672226208093043936541696 * q^64 + 2652084094607847915810184973553481440 * q^66 + 5401062423529881431761320436868275176 * q^67 + 7110274695178254111533494284632123328 * q^69 + 516103243900107216646679160954379200 * q^70 - 27544975046740790141119542770107057920 * q^72 + 30000154498324943042431295514883418136 * q^73 + 43820294796704764666539599709819928500 * q^75 - 215478934792040263381331019050660960352 * q^76 + 234946633516471169601955850003339878560 * q^78 - 128704557118405295534397879672035334840 * q^79 + 473157359902659920298963194247360443532 * q^81 - 639159997421964256448917103585883414720 * q^82 + 1283288903941350744781821238287455403552 * q^84 - 1077142486191382871466217243736209678080 * q^85 + 1076668306862385320797179121273520148960 * q^87 - 2918662713596496795370587920448329114880 * q^88 + 6571793457940570799819318674019816438880 * q^90 - 9859184204686878150356379414618151910256 * q^91 + 11506410044121210986218054652959643683416 * q^93 - 16857264118330945289191940748512432348544 * q^94 + 53068562519213731340201280418423192237056 * q^96 - 41841010071967618660163746722085070705064 * q^97 + 54341076855402233475300783474292013590080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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